Chapter 5b - Logarithms

Converting Log and Exponential Form

100

Convert to Exponential Form:

log_2(8)=x

2^x=8

200

Convert to Logarithmic Form:

4^y=x

log_4(x)=y

300

Convert to Exponential Form:

log_(x-1)(4)=2y

(x-1)^(2y)=4

400

Convert to Exponential Form:

log_(3x)(5-z)=4y

(3x)^(4y)=5-z

or

500

Convert to Logarithmic Form:

10^(x+4)=2y-7

log(2y-7)=x+4

Solving Algebraic Log Equations with Log Properties

100

Solve for x:

log_3(x-3)=log_3(55)

x=58

200

Solve for x:

log_5(x+6)=log_5(3x)

x=3

300

Solve for x:

 log_x216=3

 x=6

400

Solve for x:

3log(4)-log(x)=log(2)

x=32

500

Solve for x: (Hint the answer is quadratic, so you will need to factor to find the solutions)

2log(x)=log(3x+4)

x=4

-1 is an extraneous solution

Expanding/Condensing Logarithms

100

Condense the Logarithms:

log_3(2x)-log_3(5y)

log_3((2x)/(5y))

200

Completely Expand the Logarithm:

log((2x)/y)

log(2)+log(x)-log(y)

300

Condense the Logarithms:(use ln the same as any other log)

2ln(3)-2ln(x)+4ln(y)

ln((9y^4)/x^2)

400

Condense the Logarithms:

3log(x)-4log(2)-5log(z)+3log(3)

log((27x^3)/(16z^5))

500

Completely Expand the Logarithm:

log₇((3x^6y^7)/(7z^5))

log₇(3)+6log₇(x)+7log₇(y)-1-5log₇(z)

Evaluating Logs

100

Solve using Logarithms:

log₇49 = x

x=2

200

Solve Using Logarithms:

log₃(1/27)=

x= -3

300

Solve by Converting:

log_4(x)=-5

x=

x = 1/1024

400

Solve using Logarithms:

 

log_x(1/64) = -2

 x = 8

500

Solve using Logarithms:

log_(x+2)(16)=2

x=2